Do the headphones have a volume control on them? I'd imagine the USB dongle is only connected to the battery charge circuit +/- contacts, unless they got fancy and hooked the data pins up to allow firmware updates or something. Regardless the TV wouldn't have built in driver support.
If the TV can't change the volume level of the "External Speakers" then you'd be stuck with what is probably going to end up as a fairly loud, line level signal getting to the headphones. On my about-that-age Samsung TV (6030 series), the manual states that external speakers don't have volume or mute control through the TV.
Besides that volume issue, you might be able to do it with an analog (or SPDIF digital) to bluetooth transmitter. Some of those may have a remote control (or just knob) for volume control if the headphones themselves don't.
I am merely assuming that your TV's external speakers are only supported by analog outputs (RCA jacks?), but if the TV has bluetooth then you might need nothing added. It might support SPDIF digital output.